ENERGY CONSERVATION AND GRAVITY WAVES IN SOUND-PROOF TREATMENTS OF STELLAR INTERIORS. II. LAGRANGIAN CONSTRAINED ANALYSIS
ENERGY CONSERVATION AND GRAVITY WAVES IN SOUND-PROOF TREATMENTS OF STELLAR INTERIORS. II. LAGRANGIAN CONSTRAINED ANALYSIS
复制标题
恒星内部隔音处理中的能量守恒和重力波。
DOI：
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发表时间：
2013
期刊：
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通讯作者：
E. Zweibel
中科院分区：
文献类型：
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作者：
G. Vasil;D. Lecoanet;B. Brown;T. Wood;E. Zweibel
在许多恒星和行星内部，音速远远超过典型的流动速度。为了跟踪亚音速运动的缓慢演变，各种隔音模型试图在保留分层对流和浮力动力学的同时消除快速声波。在天体物理学中，滞弹性模型通常是经过声音过滤的分层模型中最受关注的模型。一般来说，滞弹性模型在恒星对流区等近绝热分层区域仍然有效，但可能会在恒星辐射区中常见的强亚绝热稳定分层层中分解。然而，研究恒星自转、环流和发电机需要了解对流区和辐射区之间的复杂耦合，这需要在两个区域都有效的稳健方程。在这里，我们将Brown等人开始的研究滞弹性模型的方程组的分析推广到两种类型的伪不可压缩模型。这类模型在大气应用中受到了关注，最近在白矮星超新星前体的研究中也受到了关注。我们证明了一个模型是能量守恒的，而另一个模型不是。我们利用拉格朗日变分方法将能量守恒模型推广到一般状态方程，并称之为广义伪不可压缩(GPI)模型。我们发现GPI方程很好地捕捉了恒星和其他层状系统中对流区和辐射区的低频现象，并提供了将低马赫数代码转换到该方程组的建议。
The speed of sound greatly exceeds typical flow velocities in many stellar and planetary interiors. To follow the slow evolution of subsonic motions, various sound-proof models attempt to remove fast acoustic waves while retaining stratified convection and buoyancy dynamics. In astrophysics, anelastic models typically receive the most attention in the class of sound-filtered stratified models. Generally, anelastic models remain valid in nearly adiabatically stratified regions like stellar convection zones, but may break down in strongly sub-adiabatic, stably stratified layers common in stellar radiative zones. However, studying stellar rotation, circulation, and dynamos requires understanding the complex coupling between convection and radiative zones, and this requires robust equations valid in both regimes. Here we extend the analysis of equation sets begun in Brown et al., which studied anelastic models, to two types of pseudo-incompressible models. This class of models has received attention in atmospheric applications, and more recently in studies of white-dwarf supernova progenitors. We demonstrate that one model conserves energy but the other does not. We use Lagrangian variational methods to extend the energy conserving model to a general equation of state, and dub the resulting equation set the generalized pseudo-incompressible (GPI) model. We show that the GPI equations suitably capture low-frequency phenomena in both convection and radiative zones in stars and other stratified systems, and we provide recommendations for converting low-Mach number codes to this equation set.